Parallel Kriging

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Parallel Kriging

• Jeff Pedelty
• NASAs Goddard Space Flight Center
• Greenbelt, Maryland
• Invasive Species Science Team Meeting
• 13 November, 2003

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What is Kriging?

• Spatial interpolator
• A weighted linear combination of point
  measurements that exploits structure of spatial
  auto-correlation present in the data
• Spatial structure determines the appropriate
  weights for points that are close allows for
  anisotropy
• Spatial structure is determined by modeling the
  empirical variogram auto-correlation as a
  function of the separation distance
• Kriging determines weights by minimizing the
  variance of the errors Best Linear Unbiased
  Estimator (BLUE)
• An Introduction to Applied Geostatistics, Isaaks
  Srivastava, 1989, Oxford University Press.

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Why Kriging?

• Stepwise regression is used to find the
  relationship between field samples and remote
  sensing, DEM, and ancillary data
• Residuals (predictions from the stepwise
  regression minus observed value) are calculated
  for each sample point
• Residuals are tested for spatial structure via
  viewing empirical variograms and statistical
  hypothesis testing (e.g. Morans I)
• If spatial structure exists then Kriging is used
  to estimate the residual surface for the entire
  study area
• Kriged residual surface is then added to the
  stepwise regression model to produce a final
  prediction that includes both small and large
  scale structure

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Why Parallel Kriging?

• Kriging step in USGS processing has presented a
  major bottleneck.
• Reducing the time of this computation allows
  different input variables to be considered,
  larger data sets to be incorporated, and more
  sites/locations to be modeled.
• Kriging algorithms are in general use and a
  parallel version has wide application.
• Currently using R. Reichs kriging routine (CSU),
  but we are now evaluating GSLIB package.

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Field Sampling in theRocky Mountain National Park
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An Elegantly Parallel Algorithm

• Parallelize using Domain Decomposition
• Each processor gets a chunk of complete rows

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Medusa / Frio Configuration
Frio on J. Schnases desk Linux PC w/ 1.2GHz
Athlon processor and 1.5GB memory
Gigabit Ethernet
Medusa Beowulf Cluster at NASAs
GSFC 128-processor 1.2GHz Athlon MP 1GB memory on
each dual-cpu node 2 Gbps Myrinet internal
network
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Scaling Results

• Run time scales with area kriged
• 20482 ran 16x longer than 5122
• Nearly linear scaling with processors

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Future Work

• Analysis of new datasets (big problem)
• ESTO/CT Project Milestone G requires we process
  more data over a larger area. Due July 2004.
• Cardus Nutans (a thistle) over the state of
  Colorado.
• MODIS time-series summaries as predictive
  variables.
• NOAA precipitation time-series.
• Conversion to GSLIB package is being evaluated
• Wider distribution broader user community.
• New parallel implementation would be needed.
• Cokriging?
• Use structure determined from ETM image.